Basketball fans are all familiar with terms like "hot hands," "on a roll," or "in the zone," that are used to describe players demonstrating what appears to be a streak of above-average performance. For over two decades, scientists have debated whether the phenomenon actually exists, or if basketball fans simply attribute non-random patterns to completely random data (something we humans have been shown to be very good at).

In most studies, the data proves inconclusive. But now, a team of Humboldt University researchers has revisited the debate armed with a data set larger than anyone has ever used before. Their conclusion? The hot hand phenomenon is real — but what causes it remains a mystery.

Researchers Gur Yaari and Shmuel Eisenmann examined free-throw sequences extracted from play-by-play data spanning 6,150 games over five NBA seasons. This data came out to a total of 308,862 free throw attempts, comprising 38,442 single free throw attempts; 132,917 pairs of free throw attempts taken by 712 different players; and 1529 triplets of free throw attempts taken by 251 different players. Here's what they found:

Strong evidence for the existence of a ‘‘hot hand'' phenomenon in free shots of NBA players were found. More precisely, several statistically nontrivial features of the data were found and can be summed into one concept: heterogeneity. The heterogeneous behavior was found both in ‘‘space'' (across players) and time (along one season). In particular it has been shown that

If one looks at the aggregated data he/she is likely to observe patterns that do not necessarily exist at the individual level.

The probability of success increases with the order of throw attempt in a sequence.

Even if one looks at each individual sequence separately, ‘‘hot hand'' patterns are still visible: probability of success following a success is higher than the probability of success following a failure.

These patterns could have resulted from ‘‘better and worse'' periods and not necessarily from positive/negative feedback loops.

In short — whether one looks at the aggregate (total) data or individual-player data, significant statistical evidence in support of the hot hands phenomenon is there. (For a basic introduction to why it's important to examine aggregate data separately from individual-player data, see this explanation of the Simpson's Paradox in basketball by Kent State's Darci Kracht.)

What the data does not make clear is what actually gives rise to the phenomenon. For example, when Michael Jordan drained six three-pointers in the first half of the 1992 NBA finals, was it simply the result of a "better" period of performance in Jordan's career, or did each subsequent shot give rise to changes in Jordan's physiological and psychological states, thereby changing his probabilities of success?

Eisenmann and Yaari can't be positive, but they speculate that the former is the case. Either way, the two researchers hope this study "will pave the way for studying [these] important questions concerning the 'hot hand' phenomenon."